LGRT 1685
The purpose of this talk is to provide a new PDE perspective for the celebrated Borell-Brascamp-Lieb inequality. Our approach is based on a generalized concavity maximum principle together with the large time asymptotics for a class of diffusion equations. We mainly focus on the connection between the heat equation and the Prekopa-Leindler inequality, which is a special case of the Borell-Brascamp-Lieb inequality. Our PDE proof for the general case and the equality condition will also be discussed. This talk is based on joint work with Kazuhiro Ishige and Paolo Salani.